Miracle: Difference between revisions

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'''Miracle temperament''' is a regular temperament discovered by [[George Secor]] in 1974 which has as a generator an interval, called '''secor''', that serves as both [[15/14]] and [[16/15]] semitones. In terms of [[13-limit]] extensions, it is discussed in [[Miracle extensions|miraculous, benediction, and manna]].

Miracle is an exceptionally efficient linear temperament which is a member of both the ~~marvel temperaments (→~~ [[~~Marvel~~ temperaments ~~#Miracle~~]]) and the [[gamelismic clan]]. It is quite accurate, with [[TOP]] error only 0.63 [[cent]]s/octave, meaning intervals of the 11-limit tonality diamond are represented with only one or two cents of error. Yet it is also very "low complexity" (efficient), as evidenced by the high density of [[11-odd-limit]] ratios (in bold) in the ~~following table:~~

Miracle is an exceptionally efficient linear temperament which is a member of both the [[marvel temperaments]] and the [[gamelismic clan]]. It is quite accurate, with [[TOP]] error only 0.63 [[cent]]s/octave, meaning intervals of the [[11-odd-limit]] [[tonality diamond]] are represented with only one or two cents of error. Yet it is also very "low complexity" (efficient), as evidenced by the high density of [[11-odd-limit]] ratios (in bold) in the [[#Interval chain]].

Some temperaments have [[11/9]] as a "neutral third", meaning it's exactly half of a [[3/2]] (tempering out [[243/242]]), and other temperaments (→ [[Gamelismic clan]]) have [[8/7]] as exactly a third of [[3/2]]. Miracle is distinguished by doing both of these things at the same time, so 3/2 is divided into six equal parts. This is in fact the generator of miracle temperament, called a "secor", and it represents both [[16/15]] and [[15/14]].

Miracle can also be thought of as a [[cluster temperament]] with 10 clusters of notes in an octave. The small chroma interval between adjacent notes in each cluster is very versatile, representing [[45/44]] ~ [[49/48]] ~ [[50/49]] ~ [[55/54]] ~ [[56/55]] ~ [[64/63]] all [[tempered]] together.

== Interval chain ==

{| class="wikitable center-1 right-2"

|-

! number of <br>secors

! cents value<ref>in 11-limit [[POTE tuning]]</ref> <br>(octave-reduced)

! cents value<ref>in 11-limit [[POTE tuning]]</ref><br>(octave-reduced)

! JI intervals <br>represented

|-

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Some temperaments have [[11/9]] as a "neutral third", meaning it's exactly half of a [[3/2]] (tempering out [[243/242]]), and other temperaments (in the [[gamelismic clan]]) have [[8/7]] as exactly a third of [[3/2]]. Miracle is distinguished by doing both of these things at the same time, so 3/2 is divided into six equal parts. This is in fact the generator of miracle temperament, called a "secor", and it represents both [[16/15]] and [[15/14]].

Miracle can also be thought of as a [[cluster temperament]] with 10 clusters of notes in an octave. The small chroma interval between adjacent notes in each cluster is very versatile, representing [[45/44]] ~ [[49/48]] ~ [[50/49]] ~ [[55/54]] ~ [[56/55]] ~ [[64/63]] all [[tempered]] together.

== Spectrum of miracle tunings by eigenmonzos ==

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 '''Miracle temperament''' is a regular temperament discovered by [[George Secor]] in 1974 which has as a generator an interval, called '''secor''', that serves as both [[15/14]] and [[16/15]] semitones. In terms of [[13-limit]] extensions, it is discussed in [[Miracle extensions|miraculous, benediction, and manna]].
-Miracle is an exceptionally efficient linear temperament which is a member of both the marvel temperaments (&rarr; [[Marvel temperaments #Miracle]]) and the [[gamelismic clan]]. It is quite accurate, with [[TOP]] error only 0.63 [[cent]]s/octave, meaning intervals of the 11-limit tonality diamond are represented with only one or two cents of error. Yet it is also very "low complexity" (efficient), as evidenced by the high density of [[11-odd-limit]] ratios (in bold) in the following table:
+Miracle is an exceptionally efficient linear temperament which is a member of both the [[marvel temperaments]] and the [[gamelismic clan]]. It is quite accurate, with [[TOP]] error only 0.63 [[cent]]s/octave, meaning intervals of the [[11-odd-limit]] [[tonality diamond]] are represented with only one or two cents of error. Yet it is also very "low complexity" (efficient), as evidenced by the high density of [[11-odd-limit]] ratios (in bold) in the [[#Interval chain]].
+Some temperaments have [[11/9]] as a "neutral third", meaning it's exactly half of a [[3/2]] (tempering out [[243/242]]), and other temperaments (&rarr; [[Gamelismic clan]]) have [[8/7]] as exactly a third of [[3/2]]. Miracle is distinguished by doing both of these things at the same time, so 3/2 is divided into six equal parts. This is in fact the generator of miracle temperament, called a "secor", and it represents both [[16/15]] and [[15/14]].
+Miracle can also be thought of as a [[cluster temperament]] with 10 clusters of notes in an octave. The small chroma interval between adjacent notes in each cluster is very versatile, representing [[45/44]] ~ [[49/48]] ~ [[50/49]] ~ [[55/54]] ~ [[56/55]] ~ [[64/63]] all [[tempered]] together.
+== Interval chain ==
 {| class="wikitable center-1 right-2"
 |-
 ! number of <br>secors
-! cents value<ref>in 11-limit [[POTE tuning]]</ref> <br>(octave-reduced)
+! cents value<ref>in 11-limit [[POTE tuning]]</ref><br>(octave-reduced)
 ! JI intervals <br>represented
 |-
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 <references/>
-Some temperaments have [[11/9]] as a "neutral third", meaning it's exactly half of a [[3/2]] (tempering out [[243/242]]), and other temperaments (in the [[gamelismic clan]]) have [[8/7]] as exactly a third of [[3/2]]. Miracle is distinguished by doing both of these things at the same time, so 3/2 is divided into six equal parts. This is in fact the generator of miracle temperament, called a "secor", and it represents both [[16/15]] and [[15/14]].
-Miracle can also be thought of as a [[cluster temperament]] with 10 clusters of notes in an octave. The small chroma interval between adjacent notes in each cluster is very versatile, representing [[45/44]] ~ [[49/48]] ~ [[50/49]] ~ [[55/54]] ~ [[56/55]] ~ [[64/63]] all [[tempered]] together.
 == Spectrum of miracle tunings by eigenmonzos ==